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594. FUNDAMENTALS OF
PROTECTIVE RELAYING
Modern power system relays are electromechanical,
electronic and/or computer-based devices that protect
power system equipment and apparatus from abnormalcurrents and voltages. The two fundamental relay
operations are to isolate faulted sections of the power
system while maintaining the power delivery
capability in the rest of the power system.Relays can have numerous inputs on which to determine if
a trip signal is required. Figure 4.1 illustrates the power
instrumentation is provided by voltage transformers (PT)
and current transformers (CT). DC power is needed to
supply relay power as well as to provide trip coil power for
the power circuit breaker. The 52 designation is the IEEE
standard C37.2 device number for power circuit breakers.
Batteries normally provide dc power in the event that the
station has lost all ac connections. Other inputs can modify
relay behavior to speed up or inhibit operations. Local
control is normally bi-state logic while remote
communications allows both multi-valued data (digitized
analog) as well as bi-level control. Relay communications
also allows remote control and event retrieval.This chapter focuses on the fundamentals of devices
designed to provide power system protection.Bus
Circuit
CT Breaker Power
52Line
RelayOther
PTCommunications
StationBattery
Figure 4.1: Single-Line Diagram of Relay Connectionto Power System
HISTORY OF RELAYSThe term relay normally refers to the electronic or
electromechanical device responsible for the processing
portion of the relay system. In general terms, relays
provide control to the breaker so that it has function
similar to a fuse or residential circuit breaker. Residential
circuit breakers and fuses both detect and
interrupt fault current. This requires both relay and
circuit breaker.Initially, relays were electromechanical and used flux toproduce torque that caused the breaker to open. Masoniderives a general torque equation shown in (4.1) andproceeds to demonstrate how selecting the value and sign
of constants K1 through K4 describes all fundamentalrelay operations. Positive torque results in forces thattend to close the trip contacts. Various forms of (4.1) willbe used to explain the fundamental operations of manytypes of protective relaying. Modern microprocessor-based relays still use many of the fundamentalrelationships derived from this expression.T K1 I K2 V K3V Icos() K4 (4.1)Many electromechanical relays are still being used
by utilities, industrial, and commercial facilities
today. They have limited capability and were
packaged such that separate units, called elements,
provided each control feature.Transistors and integrated circuits replaced induction
disk solid-state relays. Microprocessor relays,
introduced in the early 1980s, have completely replaced
both electromechanical and solid-state relays for new
applications.Terminology is relatively unchanged since relay
engineers were already familiar with the terminology
associated with electromechanical relays. Operate and
restraint torque do not physically exist in microprocessor-
based relays, but are derived mathematical quantities
based on microprocessor code.The purpose of the protective relay has remained
consistent over the years: to efficiently and effectively
deenergize faulted portions of the power system while
causing minimum disruption to the remaining unfaulted
sections. Relays provide the controls for automatically
switching all aspects of the power system. Normally, the
switching action is set to deenergize selected devices or
portions of the power system.Some automatic switching control provided by relayswill reclose a breaker shortly after a trip in an attempt to
quickly restore power to a circuit. Such reclosing
operations are based on the experience that a high
percentage of some types of faults are transitory and self-
clearing after the line is deenergized. Relays have
evolved to control, record, report, communicate, and in
some cases, adapt to, events on the power system.
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60TYPES OF RELAYSRelays are designed to protect every kind of apparatus
and facility used in the generation, delivery, and
consumption of electrical energy. Elements commonly
protected by relay equipment are listed in Table 4.1. In a
coordinated protected system, the effects on both theprimary zone of protection and the adjacent zones must
be carefully planned. In addition to the variables listed in
Table 4.1, relays also monitor local and remote status
contacts controlled by relays and switches.Table 4.1: Protected Power Systems and Parameters
MeasuredParameters Measured
V I F T PtRotating Generators M M M M MDevices Motors M X M
Synchronous M M M M MCondensers
Lines & Transmission M M D D M MCircuits Distribution M M D D M
Cable M M D D MSeries M M MCapacitorsShunt Reactor M M M M
Station Breaker M M M MFailureBus Fault M M MTransformer M M MShunt M M MCapacitor
System Load Shedding M M D DStability Load / M M D D
FrequencyControlReclosing M M D DSync Check M M D D
Parameter symbol code:VVolts MMeasuredIAmps DDerivedFFrequency tTimePhaseTTemperaturePPressure
Relays that run autonomously or without local and
remote supervision make trip/no-trip decisions based on
local analog measurements and status contacts.
Supervised relays are capable of autonomous operation
but perform better when based on remote information
using some means of communication. The supervision
can block or permit trip operations or provide status.Supervised relays can perform faster and more securely,
but are also more likely to fail.4.1.1 Protecting Lines and CircuitsThe three most common types of line relaying are
overcurrent, impedance, and phase comparison, which
includes pilot wire relaying. Another type, based on
traveling wave theory, is less common. Derive the
frequency and phase relationship between voltage and
current for the relay algorithm from the measurements
of voltage and current (see Table 4.1).For dependable and secure functionality, the relay must
be able to determine the direction and relative distance
to the fault. From the relay perspective, fault direction is
forward if the fault occurs in or beyond the zone of
protection, as illustrated in Error! Reference source
notfound.. Sometimes the direction is implied, such as
withsingle source radial feed networks. Section 4.1.4
discusses various methods of deriving direction.
Distance is an abstraction of the impedance between the
point or relay instrumentation and the fault. It is only
possible to measure physical distance to the fault if a
relationship of ohms per mile is identified. For
additional information on fault locating see 4.3.4.
Determine distance from current measurements by
assuming the source voltage is constant. More accurate
measures of distance require voltage measurements and
knowledge of line impedance (see line constants
parameter program).Relays frequently address phase-to-phase or simply
phase faults separately from phase-to-ground faults
(also called ground faults). This is because the detection
algorithms are separate in order to tune or maximize the
relay to the particular type of fault.4.1.2 Overcurrent Relays4.3.2.1 Instantaneous Overcurrent Relays
(ANSI Type 50)
Model overcurrent relays similarly to overvoltage relays,
using a modified form of Masons general torque
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61equation as described by (4.2). The relay requires
positive torque to operate. Negative K4 provides
constant restraining. Solving to the balance point (zero
torque) determines the trip current, also commonly
called pickup current, as shown in (4.3).T K1 I
2 K4 (4.2)I
PU K4 , a constant (4.3)K1
The induction disk electromechanical relay produces
torque in a moveable disk similar to the disk in a
residential electrical meter. Consider the case when two
time-varying fluxes of the same frequency but different
phase, , as expressed in (4. 4) and (4. 5) are imposed on
a disk as shown in Figure 4.2.1 1Msin(t) (4. 4)2 2Msin(t ) (4. 5)At the instant when both fluxes are directed downward
and are increasing in magnitude, each flux induces
voltage around itself in the rotor, and currents flow in the
rotor under the influence of the two voltages. The current
produced by one flux reacts with the other flux, and vice
versa, to produce forces that act on the disk. Assuming
that the disk currents produce insignificant self-
inductance, currents i1 and i2 are in phase with their
voltages, resulting in (4. 6 )and (4.7). This produces two
mechanical forces opposite in direction so the net force
is the difference shown in (4.8).d1
(4. 6)i1 1Mcos(t)dtd2
(4.7)i2 2M cos(t)dt
F F2 F12 i11 i2 (4.8)Substituting the quantities of (4. 4) through (4.7) into
(4.8) results in the net force. The result is (4. 9), which
reduces down to (4.10), which shows the force is
proportional to the magnitude of the product of the twofluxes and the phase difference between them.F1M2Msin(t) cos(t)cos(t) sin(t) (4. 9)F1M2Msin() (4.10)Figure 4.3 shows the basis of both the residential electric
meter and the induction disk relay. The pole shading
forces a phase shift in the flux, , that produces the force
in (4.10). Since torque is a force times a distance and
since the applied current produces identical flux for1
and 2, (4.10) can be expressed as (4.1) whereK1
accounts for all the proportionality.
Disk
F2
F1
Figure 4.2: Induced Currents and Forces Resulting FromTwo Flux Paths on a Metallic Disk
To complete the comparison of the induction disk relay
to the residential electric meter, meter the power
assuming a constant voltage and no restraining spring.
This makesK4 zero in (4.2). The meter is free to rotate at
a speed proportional to the square of the load current. A
counter simply measures the number of disk rotations
and applies a kWh conversion per disk revolution.
ShadingSource Ring
RotorDirection Shadingof force Ring
Figure 4.3: Shaded-Pole Induction Disk4.3.2.2 Time-Overcurrent Relays (ANSI Type 51)The overcurrent relay more or less approximates the
operation of the thermal fuse. This similarity is a design
characteristic of time-overcurrent relays to
accommodate systems that integrate fuse protection with
electromechanical, electronic, and microprocessor-based
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62relays. For time-overcurrent relays, the magnitude of the
applied or operating current determines the time to
operate. Electromechanical devices had a disk that
looked much like the ones in a conventional residential
power meter. Figure 4.4 illustrates some of the
mechanical components of the induction disk
overcurrent relay.
Time DialDirection Setting
ofCurrent
InducedTorque
ResetRestraining Position
SpringDisk
location, and t0 to when the ratio ofIPU/Iis greater than
unity, the trip time is the time required to rotate the disk
through the angle determined by TDS as shown in (4.14)
and (4.15).
I 2 Ts 1Kd (4.11)
p t
I 2 s
1Kd (4.12)
p t
where:s is the restraining spring torque
I is the applied currentIPU is the pickup current that is established by thezero torque from (4.3)Kd is disk damping factor due to magnetic drag
is the disk rotation angle TDSFigure 4.4: Diagram of Induction Disk RelayA restraining spring forces the disk to rotate in the
direction that opens the trip contacts while current
creates operating torque to close the contacts. The net
torque equation is expressed by (4.11), where positive
torque closes the contacts. The IPU relay setting fixes the
value of the pickup current. When the current applied to
the relay equals the pickup current, the contact closing
torque just equals the restraining torque and the disk will
not move regardless of its position. If the applied currentincreases above the pickup current, the disk will begin to
rotate so that the trip contacts come closer together. If
I 2 s t2 t121 1K I
d
I 2 s trip timeTDS 1d p
Kdtrip time TDS s TDS
I 2
1I p
(4.13)
(4.14)
AM2 1 (4.15)
the operating torque equals the restraining torque then
the net torque in (4.11) is zero. This allows us to solve
the torque balance equation shown in (4.12).iiIntegrating (4.12) with respect to time, (4.13) shows
that the rotation angle depends on the magnitude of the
current and the time that the current is applied. The trip
contacts, positioned with an adjustment called the time
dial setting (TDS), determine how far the disk must
rotate to close the contacts. The TDS units vary
continuously from zero to a value typically greater than
10. The relationship of TDS to the time to operate is
such that increasing the TDS setting by a number
increases the time to trip by that same amount. For
example, changing the time dial setting three to nine
makes the time to operate three times longer.Damping magnets and coils impedes the speed of
rotation. Referencing the initial disk position to the reset
where: M is the multiples of pickup current = I/IPU
and A = Kd/s.Equation (4.15) demonstrates that three parameters
determine the operating characteristics of the time-
overcurrent relay, namely the pickup current, IPU, the
time dial setting, TDS, and the degree of inverseness.
For the development shown in (4.11) through (4.15), the
constantA and the power ofMin (4.15) establish the
degree of inverseness. In practice, there are actually
three parameters that determine the degree ofinverseness. (4.16) and (4.17 show the form usually used
to describe time-overcurrent relay operations. (4.16)
represents the reset time and (4.17) the time to trip. This
tripping time is only valid if the relay is the reset
condition. Similarly, (4.17) is accurate only if the relay
starts when the time-overcurrent function has timed out.
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63Some sources claim that (4.15) and (4.17) include disk
inertia by using the parameter B. The result is that relay
manufacturers design relays with particular
characteristics using various factors forA,B, andp.iii
Although it is not required, most manufacturers facilitate
relay coordination by using the standard values shown in
Table 4.2 for inverse characteristics. Figure 4.5illustrates the family of curves for very inverse
characteristics and a time dial setting of one through ten.
This set of curves demonstrates that the time to operate is
linearly dependent on the time dial setting for a given
characteristic and multiple of pickup current. A complete
set of I.E.C. and U.S. standard curves based on the IEEE
standard C37.112-1996 can be found in appendix. C
(4.16)tr TDS 1 M
A for M 1. (4.17)tt TDS B pM 1
Table 4.2: Degrees of Inverseness as a Function of A,
B and p for U.S. and I.E.C Standard CurvesCurve A B C P
U.S. Moderately 0.0104 0.2256 1.08 0.02inverse (U1)U.S. Inverse 5.95 0.180 5.95 2.00(U2)U.S. Very inverse 3.88 0.0963 3.88 2.00(U3)U.S. Extremely 5.67 0352 5.67 2.00inverse(U4)
U.S. Short-time 0.00342 0.00262 0.323 0.02inverse(U5)I.E.C. Class A 0.14 0.0 13.5 0.02Standardinverse (C1)I.E.C. Class B 13.5 0.0 47.3 2.00Veryinverse (C2)
I.E.C. Class C 80.0 0.0 80.0 2.00Extremelyinverse (C3)I.E.C Long-time 120.0 0.0 120.0 2.00inverse (C4)I.E.C Short-time 0.05 0.0 4.85 0.04inverse (C5)
Figure 4.5: Family of Curves for U.S. Inverse U2
CharacteristicsBenmouyal and Zocholl discuss time-current
coordination in systems that use both thermal fuses and
time-overcurrent relays.ii The basic concept is that the
higher the current, the faster the relay or fuse operates.
Figure 4.6, reproduced from this reference, illustrates
how the 50E fuse time-current characteristics compare
with the extremely inverse relay characteristics. The
shapes of these curves are well defined in IEEE standard
C37.90. Fuses are generally used to clear specific loads
or sections of a distribution system and are located on
poles and in service entrances. Thermal fuses are rather
inexpensive, but are destroyed in the process of clearing
the fault. A worker must replace the fuse before service
can be restored.Breakers and other interrupting mechanisms are more
expensive than fuses and are usually installed at the
substation. As the cost of breakers declines, the trend is
to replace fuses with relays and interrupters. Time-
overcurrent relays discriminate faults by current
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64magnitude and use time to coordinate operations in
different zones. So the closer the fault, the faster the
relay will operate. Faults farther away have higher
impedance between the source and the fault, resulting in
lower fault current and therefore longer operating times.
For radial lines (lines with only one source) and with
downstream fuses, the additional time allows the fusesto operate first. Relay-fuse coordination is important to
minimize the extent that clearing the fault will
deenergize the power network.Figure 4.7 compares the time to operate as a function of
multiples of pickup current for three different inverse
characteristics. (4.16) and (4.17), together with Figure
4.5 and Figure 4.7, lead to several observations. One is
that the time to operate is roughly inversely
proportional to the inverse of the square of the current,
making it responsive to energy. Another is that after 20
multiples of pickup current, the time to operate is nearly
independent of current.Fuses are nondirectional single-phase devices and
should not be used where the loss of one phase could
damage equipment. Since fuses are generally sized for
load, increase the fuse rating, and in some cases, the
hardware, if adding load. Figure 4.6 shows a shaded area
between the minimum melting time and the maximum
melting time. Fuses have unpredictable performance
whenever currents are in this region whether or not the
fuse opens. Fuse coordination with upstream relays
requires that the relays not operate faster than the
maximum melting time in addition to time for fusetolerance variations. The difference between the relay
and fuse operating times for a specified fault current is
the coordination time interval (CTI).A repeated high surge of high current for which the fuse
does not operate still causes the fuse to heat up.
Coordination is useless without sufficient time to cool
between applications of high current.
Figure 4.6: Extremely Inverse Relay Characteristics
Compared With Minimum and MaximumClearing Times of a 50E Fuse
Figure 4.7: Comparison of Inverse Characteristics for
Modified Inverse, Very Inverse, and
Extremely Inverse CharacteristicsAs previously stated, time delay with relays allowscoordination between other time overcurrent relays as
well as fuses.iv Consider a faulted single feed system as
illustrated in Figure 4.8. The relay on the faulted line,
R4, should be the only relay to trip. (4.18) determines the
maximum three-phase fault current that can be expected
for a fault beyond bus #3 and, if the longest line leaving
Bus #3 has impedance Z4, (4.19) expresses the minimum
fault current. Similar expressions developed
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65for each line segment show that the closer the segment is to
the source, the more the expected current for a fault on a
particular segment increases. Achieve coordination by
increasing the time dial settings while proceeding toward
the source. If relay R2 should provide backup protection for
relay R4, then set R4, the relay with the greatest source
impedance, with the lowest time dial setting. Chapter 5discusses relay coordination and coordination for
distribution protection in more detail. Relay-relay and
relay-fuse coordination should never be attempted for fault
currents under1.5 times for pickup current because errors
are greatly magnified and performance is not repeatable.
Set the pickup above load but sensitive enough to see faults
up to the next protection device. IfIMINis defined as the
minimum fault current, then set thepickup current at least
as low as the current but above maximum load current. For
relays R2 and R3, set the TDS to trip no faster then the next
downstream device when the fault current is maximum for
an out of zone fault. For example, if current,I4MAX, resultsfrom a fault is immediately downstream of R4, then set the
TDS for relay R3 slower than that of R4 when the R3
current isI4MAX,plus the maximum expected load current at
Bus #3.I
f
3MAX
VsZ1Z2Z3 (4.18)
If3
MIN
Vs
Z1Z2Z3Z4 (4.19)Bus Local Bus Local Bus
#1 Load #2 Load #3Source Local
Vs LoadZ1 Z2 Z3Faulted
Z4Line
R2 R3R4
Figure 4.8: Single-End-Feed Power Network4.2.7.2.1 Time-overcurrent relay dynamics v,xivThe previous discussion on the trip times for time-
overcurrent relays assumes that the line current is
constant for the duration of the fault. Historically,
coordination studies make that same assumption. To
assume otherwise requires engineering tools capable ofincluding the transitory dynamics and a means of
predicting the sequence and magnitude of the dynamics.
First ignore the transient dynamics and determine the
fault current magnitude and phase with a single solution
using Ohms law to solve one or a set of simultaneous
equations with complex variables. The computations are
always made after the system is at steady state.
Since the 1960s, digital computers have analyzed power
systems using time domain solution techniques,
generically called EMTP or electromagnetic transient
programs. Figure 4.10 and Figure 4.12, discussed below,
show the results of such simulations. Time domain
solutions use difference equations with algorithms that
approximate numerical integration and differentiation.Equation (4.13) shows a mathematical relay model that
can be rewritten as shown in (4.20) and subsequently
modified into a difference equation as shown in (4.21).
Equation (4.21) uses the same definitions for A, B and p
that are used in (4.17).I ps t2 t112 1 (4.20)K I
d
1 Mnp 1 n Tn1 . )
TDS
BMn
p1A
Where Mn = In/Ip and In is the magnitude of most
recent current sampleThe single line diagram in Figure 4.9 represents a
simulation of a 250 resistive fault initiated at 8.3 ms
that progresses to a 25 fault at 62 ms. A tree branch
coming in contact with the wire could cause this type of
fault. The power system to the left of the 230 kV-
transmission line is a lumped parameter Thevenin
equivalent impedance and source. The two time-
overcurrent (52) relays in this system are modeled
identically except that the time dial setting is 2.4 for theS bus relay and 1.0 for the R bus relay.
Bus RBus S
SourceXfmr
ImpedanceBreaker Breaker
Gen 230KV 69KV25
52 52Fault #2C-G
225Fault #1
C-GFigure 4.9: Single-Line Diagram of Simulated Faulted
Power System With TOC RelaysFigure 4.10 simulates the response of an
electromechanical type 52 relay at location Bus R to a
phase-C-to-ground fault starting at the time of the initial
250 fault. The bus R phase current curve on this graph
is the time domain phase-C current. The current
magnitude algorithm computes the peak value of the
phase domain current. The disk position curve is scaled
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66so that 100 corresponds to the reset position and zero
to the trip position.The bus R phase current in Figure 4.10 shows that the
current waveform is significantly offset immediately after
the fault is initiated. The algorithm that computes the
magnitude determines the transient response of the currentmagnitude to the step increase. Although the current is
almost fully offset, the relay response verifies that the
computer algorithm filters out the offset component. The
change of slope after the second fault is initiated is in
response to the higher fault current that causes the disk to
rotate faster. The steeper slope of the disk position line
indicates this. Approximately 115 ms into the simulation,
the contacts are trip closed but the line current continues to
flow. The breaker-operate time for this simulation is 40 ms
and the current will stop only at a current zero crossing.
After the breaker opens, the response of the algorithm to the
step change in current causes a transient response in the
current magnitude.
relay at Bus S is three times that of the relay at Bus R,
we set the reset value three times higher. Because this
relay did not trip, the additional load at Bus R causes
line current to continue flowing after the Bus R switch
opens. This example does not clearly show the
differences in slope of the disk position that indicate the
speed of the relay disk even though the current at Bus Sincludes the load.The simulation also shows the disk on the Bus S relay as
continuing to rotate after relay Bus R has already made
the trip decision at 115 ms. In fact, the simulation shows
that the rotation of this relay did not reverse until almost
190 ms. For this example, the breaker-operate time, set
to 40 ms, is the biggest contributor to the persistence of
fault current processed by the Bus S relay. Even though
the fault current is interrupted at about 160 ms, the disk
continues to rotate in a trip direction. Both
electromechanical and microprocessor relays have this
problem, although the causes are different. In
electromechanical relays the cause is disk inertia; in
microprocessor relays it is algorithm transient response.Figure 4.11 and Figure 4.12 demonstrate the importance of
coordinating relay operating times. As relay performance
and breaker-operate time become shorter and more
predictable, the tendency is to reduce CTI to speed the
clearing of faults near the remote terminal. The problem
with using short CTI times is that maximum loads must be
predictable or the fault current, in addition to load, may
cause the relay at Bus S to operate even though the fault
has already been cleared.
Figure 4.10: EMTP Simulation of a Faulted Power Systemand Operation of a Time-Overcurrent RelayWith Trip Output
The relay begins to reset once the relay current is belowthe pickup value. The restraint spring torque and thetime dial setting fixes the reset time forelectromechanical relays. Slow reset time can causecoordination problems, called ratcheting, during reclose
operations. If a reclose operation occurs before the faultclears and the relay is fully reset, then the time to trip is not predictable. Microprocessor relays are able to usevery short reset times. Figure 4.11: 52 Relay Operation at Bus S for Light Load at
Bus RFigure 4.11 shows the Bus S relay response to thesame fault. The plotted disk position for both relays
demonstrates the effect of the TDS. Since TDS for the
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67
Figure 4.12: 52 Relay Operation at Bus S for Heavy Loadat Bus R
4.2.7.2.2 Zero-Sequence Overcurrent ProtectionTo obtain sensitive ground fault detection, use a relay thatresponds only to the zero-sequence current of the system.
A zero-sequence overcurrent relay simply measures the
sum of the three phase currents, as shown in (4.22).
Unbalanced faults involving ground, such as phase-to-
ground or phase-to-phase-to-ground faults, cause zero-
sequence current, also referred to as ground or residual
current. CT connection configurations and the neutral
current of a delta-grounded wye transformer are
additional sources of zero sequence current. Set zero-
sequence overcurrent elements at very sensitive levels
(i.e., a low pickup setting) because the zero-sequence
current generated under load conditions is typically small
compared to load currents.Ir Ia Ib Ic (4.22)A common misconception is that zero-sequence current
only exists under fault conditions. However, zero-sequence
current can and does exist under no-fault, normal load
conditions. Unbalanced system conditions, such as those
caused by nontransposed transmission lines or unbalanced
loading, can cause zero-sequence current to flow.Never set
ground fault protection elements tobe more sensitive than
the normal system unbalance.Doing so results in
unintentional relay operations. This setting limitation meansthat load or system induced zero-sequence current can
severely impact the sensitivity of a zero-sequence
overcurrent element.vi
Fault studies make zero-sequence fault quantities readily
available. It is also very simple to determine pickup
thresholds from fault study data. Because the majority of
fault studies today also model intercircuit zero-sequence
mutual coupling, zero-sequence currents from
these studies already account for these effects.Zero-sequence overcurrent elements can provide very
effective resistive ground fault coverage, either
independently with time delays or in pilot tripping
schemes. Sensitive zero-sequence overcurrent elementsin pilot tripping schemes provide the best, high-speed,
resistive fault coverage.Advantages Of Zero-Sequence Overcurrent ElementsCompared to using phase elements for ground protection,
zero sequence overcurrent elements: Provide outstanding resistive fault coverage
Are easy to set, understand, and visualize
Are not affected by load flow for balanced lines
and loads
Are not affected by phase-to-phase or delta-
connected load (i.e., delta-wye transformers) Complications Of Zero-Sequence Overcurrent ElementsZero-sequence overcurrent elements are affected by:
Changes in the power system source
Zero-sequence mutual coupling
Normal system load unbalance
In-line switching and open-phase conductors,which can have a negative impact on the security
of a pilot scheme
4.2.7.2.3 Negative-Sequence Overcurrent ProtectionNegative-sequence overcurrent elements have been
gaining popularity as a method for detecting high-
resistance ground faults. In the past, protection schemes
using negative-sequence current elements were difficult
to implement and complex in design. Many relays now
offer negative-sequence current elements as a standard
feature. Some utilities are using negative-sequence
overcurrent elements to improve the sensitivity of theirprotection schemes.Negative-sequence currents can arise whenever any
system unbalance is present. Faults, nontransposed lines,
and load unbalance are major sources of system
unbalances. As with zero-sequence overcurrent elements,
system unbalances can significantly impact the
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68settable sensitivity of a negative-sequence overcurrent
element.The negative-sequence current depends on phase
rotation. (4.23) gives the negative-sequence
current, which is derived from the three phase
currents and assumes an ABC phase rotationresulting in the transposition of terms IB and IC.I2 Ia a2 Ib a Ic where
3 4.23)a 1120 and a
21240
For faults at the remote ends of long lines, negative-
sequence current elements provide better resistive fault
coverage than zero-sequence current elements because
they are not affected by intercircuit mutual coupling.
The negative-sequence impedance of a transmission line
is significantly less than the zero-sequence impedance.
Faults at the remote end of a long line typically havemore negative-sequence current than zero-sequence
current, depending on fault location and network
configuration. Immunity to mutually coupled currents is
equally important for distribution lines built under
transmission lines.Advantages Of Negative-Sequence OvercurrentElementsCompared to using phase elements for ground
protection, zero sequence overcurrent elements:
Outstanding resistive fault coverage Better resistive fault coverage than zero-
sequence overcurrent elements for faults at the
end of long lines (for some line configurations)
Insensitive to zero-sequence mutualcoupling associated with parallel
transmission line applications
Not affected by load flow because the loadcurrent has very little impact on the negative-
sequence current magnitude
Preferred over zero-sequence overcurrent elementsfor wye-connected loads
Complications Of Negative-Sequence OvercurrentElements
Affected by changes in the power system source
Affected by normal system load unbalance
Affected by in-line switching and open-phase
conductors, which can have a negative impact on
the security of the pilot scheme
Required to coordinate with phase and groundfault detecting elements
4.2.7.2.4 Directional Control of Negative- and Zero-Sequence Overcurrent Elements
The previous discussion on zero- and negative-sequence
overcurrent elements only considered the operating or
tripping quantities. These elements must be supervised
by directional elements when used on multisource
systems. In this text, directional control means that the
input to the computing algorithm is enabled or disabled
by the direction element as Figure 4.13 illustrates. The
directional overcurrent relay can be a type 50
instantaneous element controlled by a type 32
directional, as illustrated in Figure 4.13b.Using directional control eliminates a race condition that
tends to cause relays to trip incorrectly. The following
example illustrates the race condition for directional
supervision. Consider the two-source system shown in
Figure 4.14 that has a fault close to Bus R. If source Er
is weak, then the contacts of the relay on Line #1 at Bus
R may be closed when breaker 4 opens. The directional
supervision contact inhibits that relay from tripping
breaker 2. After breaker 4 opens, current from Er causes
the current direction to change because fault current is
now from Bus R via Bus S. If the dropout of theovercurrent element is slower than the pickup of the
directional element, breaker 2 will trip. ixReference DC Bus + Reference
DirectionalSignal Signal DirectionalPhase Element 32 32 Phase Element 32Current Current
DC Bus +Overcurrent
50/ Overcurrent 50/Element 50/51 32 Element 50/51Phase 51 51(50 or 51) Phase (50 or 51)Current Current
52 AC Circuit 52 AC CircBreaker Break
a. Directional Supervision DC Bus - b. Directional Control DC Bus -Figure 4.13: Circuits Showing the Difference
Betweena. Directional Supervision and
b. Directional Control
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69Bus S Bus R
Line #23 4
Es R R ErFault
1 Line #1 2R R
Figure 4.14: A Case for Directional ControlThere are several methods for determining the correct
direction of ground fault current. Zero-sequence voltage
and current reference quantities are the most common.
Negative-sequence voltage is also used for directional
polarization. Section 4.1.4 discusses these methods in
detail.4.3.2.3 Directional Stepped-Time Overcurrent
(ANSI Type 67)
If the type 67 relay element is to provide backup
protection, use definite time delay for downstream
coordination. The 67 element requires more attention to
detail for coordination than type 51 relays. Figure 4.15
compares the stepped-time delay characteristics to the 51
relay continuous time delay characteristics. The
advantage that the stepped-time has over the 51 is that
the time steps are independently set. The disadvantage is
that overreach errors have a more pronounced effect that
often proves difficult to coordinate.Bus S 51 Increasing
67 timeG 1 2 Load 5
F1 F2 F3 F4Load Load Load Load
1 2 3 4Figure 4.15: Comparison of Stepped-Time (67) and I2t (51)
Time-Overcurrent Relaying4.1.3 Instantaneous Overvoltage relaysOvervoltage conditions can harm equipment by breaking
down insulation, leading to a low-impedance fault to
ground or to another circuit. Transient overvoltages are
generally more severe than steady-state overvoltage
conditions and rarely persist for more than a few cycles.
Switching operations, faults, and lightning can cause
transients. Surge or lightning arresters can limit the voltage
at equipment terminals. The energy that can be dissipated
by surge and lightning arresters is limited, but should be
designed to exceed the energy in a potential transient. If
not, the arresters will be damaged or destroyed leaving the
circuit without further protection.Arresters operate by flashing or generating a momentary
low-impedance path to ground. As Figure 4.16
illustrates, the circuit inductance limits the instantaneous
current. If the circuit impedance between the source of
the voltage transient and the arrester is too small, then
the arrester may fail if the current exceeds arrester
capability. Such would be the case if lightning were to
directly strike the terminals of a transformer. The
resistance, inductance, and capacitance shown in Figure
4.16 represent the line, bus, or conductor model and not
any actual equipment or device, although those can also
be added to the analysis.Circuit Impedance
PowerEquipment
Voltage SourceArrester
Figure 4.16: Arrester Circuit for Transient SuppressionSpark gap arresters and metal oxide arresters are two
primary types of devices for transient overvoltage
protection. Protective spark gaps are crude protection
devices consisting of air gaps between electrodes of
various shapes. The physical distance separating the line
electrodes and ground points sets the flash-over voltage.
Environmental conditions such as humidity, airborne
dust, and contamination can affect the accuracy of this
setting. The voltage across spark gap arresters drops to
almost zero when flashed over. The circuit must be
deenergized for a number of 60 Hz cycles to extinguish
the arc across the arrester that sustains the low-
impedance path to ground. Since the arc across the gap
constitutes a line-to-ground fault, some type of
overcurrent protection usually deenergizes the line.The operating characteristics of arresters are similar to a
reversed biased zener diode. Little or no current flows
through the device until the voltage across the device
terminals exceeds the spark over voltage. Then current
increases nonlinearly while voltage remains constant.
The advantage of metal oxide arresters over spark gaps is
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70that the line does not need to be deenergized to reset
the transient protection.Incorrect operations or anomalies such as
subsynchronous resonance cause steady-state
overvoltages. The duration of these events would soon
destroy transient protection devices if they operated.(4.24) expresses the modified version of Masons
generalized torque equation for a spring-restrained
electromechanical overvoltage relay. (4.25) is the
solution of (4.24) for the balance or zero torque
condition. The solution shows that if the voltage is
greater than a threshold equal to K4/K2, then sufficient
torque is produced to overcome the restraining spring
and close the contacts.T K2 V K4 (4.24)V
K4a constant (4.25)K2
4.1.4 Direction (ANSI Type 32)The concepts of direction were previously introduced
without discussing how direction is determined. The
sections that follow discuss various polarizing signals.
These signals provide a dependable phase reference that is
compared to the operate quantity affected by the fault to
determine direction. The amplitude of the polarizing
reference is not critical as long as there is enough
magnitude to reliably determine the phase angle.Fault direction relative to the relay instrumentation is
either forward or reverse. Without direction control,
relays will overreach, tripping incorrectly and
unnecessarily deenergizing parts of the power system.
The results of this type of incorrect operation can range
from nothing at all to a significant loss of revenue
caused by regional blackouts. The cost of incorrect
operation depends on the generation, load, and system
configuration at the time of interruption.The arrival time of the fault signature determines
direction in traveling wave relays. For conventional 60
Hz signal-monitoring relays, the phase angle
relationship of the polarizing and operating quantities
that are typically voltages and currents determines
direction. Determining direction requires a phase
reference that is independent of load and fault type.Radial systems do not require direction supervision on
protective relays because fault current can only be
supplied for one direction. Hence relays are set to look
toward the load. Systems with multiple sources have
relays that look at the same zone of protection from both
directions. Figure 4.17 shows a single-line diagram for
such a system.Directional elements have a sensitivity limit to guarantee
sufficient voltage and current amplitude to reliablydetermine the direction of current flow. The directional
element controls the input to the detection element. This
requires that the type 32-element be set to be slightly
more sensitive than the detection element. For ground
relaying, the sensitivity of the 32 should be set above the
expected maximum load. Setting the sensitivity above
load is desirable for phase relays, as well, but not always
possible. If the type 32-element is used to detect faults
behind Zone 3, the relay for pilot relay schemes, then
the sensitivity of the Zone 2 for the remote relay should
always be less than the sensitivity of the local Zone 3.
Failure to follow this rule will result in misoperations at
the remote terminal.Is Ir
Es Zs ZLs ZL*m ZL*(1-m) Zr ErF2 Rs Vs,Is F1 Rr Vr,Ir
Figure 4.17: Dual Source Single-Line System for TwoNonsimultaneous Faults
4.3.2.4 General polarizing conceptsFor protective relaying, the polarizing signal should becontinuously available and should be valid regardless of
fault type and distance. Torque equations, generally in the
form of (4.26), will determine fault direction; positive
torque results from forward faults and negative torque from
reverse faults. Schweitzer and Roberts demonstrate that
(4.27) is an equivalent expression but is more
computationally efficient in microprocessor-based systems
that use rectangular representations of complex variables.vii
No single approach works equally well for all types of
faults and line configurations.viii
Therefore, computer-
based relays frequently use multiple schemes in
combination with a fault type selection to make the bestdetermination of the fault direction. Examples of the ten
possible fault types, as well as candidates for polarizing are
presented in the appendix.T Vpol Iop cos(VpolIop) (4.26)whereIop is the current of the faulted phase.
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71
TRe Vpol (4.27)Iop4.3.2.5 Fault-Based Available Polarizing Signals xBoth phase and symmetrical component voltages and
currents can provide a reference signal for polarizing.The degree that the faulted phase voltage collapses
depends on the source impedance, the impedance
between the relay, and the fault, as demonstrated in
Figure 4.18. This plot shows that the phase voltage has
its maximum value at the sources at both ends and
decreases to a value equal to the fault current times the
fault resistance. Therefore, determining direction when
the fault is close to the relay or the source impedance
behind the relay is significantly more than the fault
resistance and the line impedance to the fault requires
polarizing quantities with memory.Conversely, the symmetrical component voltages for
nonsymmetrical faults are zero at the sources and are
maximum at the point of the fault as shown in Figure
4.19. The horizontal axis in both Figure 4.18 and Figure
4.19 represents either distance or increasing impedance.
The generation of straight-line voltage profiles assumes a
linear distribution of impedance as a function of
distance. Represent discrete lumps of impedance, such as
would be encountered in transformers, by vertical
changes in voltage. Hence, symmetrical component
voltages produce better polarizing quantities for
nonsymmetrical faults close to the relays, whereas self-
or cross-polarizing phase voltages are better for distant
and/or high impedance faults.Max.volts
Mg
nit
ud
ePositive- sequence or
Line
Voltag
e
phase voltage
profile0 volts
Vs Impedance Vr Ersto Es
Fault locationFigure 4.18: Phase Voltage Profile for Line-to-
Ground Faults in a Two-Source
System
Max.Zero- and negative-
voltssequence voltage
S
equence
V
oltageMagnitude
profile
0 voltsVs Impedance Vr ErEs
to EsFault location
Figure 4.19: Zero- and Negative-Sequence VoltageProfile for Line-to-Ground Faults in aTwo-Source System
Phase and symmetrical component currents do not
change, regardless of fault location or source impedance,
provided there are no other branches in the circuit. Inother words, the representations of Figure 4.18 and
Figure 4.19 are true as long as there is only one current.
However, this is rarely the case. Even the mutual
couplings by inductance and capacitance constitute
additional paths that current can take. More commonly,
tapped loads and parallel circuits provide alternate paths
for the current to travel.4.2.7.2.5 Self-Polarizing and Memory CircuitsSelf-polarizing directional units do not work well for
line-to-ground faults close to the point that the voltage is
measured because it is difficult to determine the phase of
low amplitude signals. Hence relays use a memory
voltage. Electromechanical relays use a parallel LC
circuit designed to resonate at 60 Hz. Computer-based
relays use a digital filter that implements an algorithm
similar to (4.28), which produces a response to a loss of
signal, as shown in Figure 4.20. The signal is sampled
synchronously, which means that the sample rate is an
integer multiple of the nominal frequency of the input
signal. Such memory filters slowly track changes in
amplitude and phase while providing sufficient signal for
signal processing when a fault occurs. Figure 4.20
demonstrates that there are zero degrees of phase shiftbetween the filter input and output. Since only the phase
is important for polarizing signals, the amplitude of this
signal is not critical provided there is enough signal to
determine the phase. As Figure 4.20 shows, there are
multiple cycles of signal after the input is set to zero.
There is also a transient response once the signal is
asserted again, so recapturing the phase of the signal
takes time. Relay logic must compensate for the time lag
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72between energizing the system and the availability of a
valid polarizing signal. The closer a1 is to unity, the
longer the memory. Many popular relays using memory
polarizing use a fast charge such that after the loss of
potential, the coefficient a1 is set to zero (hence no
memory) forNsamples as illustrated in Figure 4.21.VMEM VIN a1 VMEM z
N
2,
Hz 1
1 a1 z 2
N = number of
samples per
cycle of a
synchronously
sampled signal,
z-1
, is the unit
delay operator,
and 0 < a1
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73Vc
VaFVa
MEMIloadIN IloadOUT
IaF2 IaF IaF1Vb
Figure 4.23: Effects of Load Current on High-
Impedance FaultsCROSS POLARIZINGUse cross-polarized signals to polarize ground-fault
detecting elements for single-line-to-ground faults. Theseelements use the unaffected phases to form the polarizing
reference. However, use special consideration when
employing single-pole tripping because the reference
phase may already be open when a second fault occurs
that needs the reference of that particular phase. As with
other polarizing approaches, fault type identification is
critical for proper operation. Roberts provides a
comprehensive analysis of approaches to directional
element implementations and provides the data shown in
Table 4.3. xTable 4.3: Cross-Polarized Fault Table
Faulted Phase Operating Polarizing QuantityQuantity (Iop) (Vpol)
A Ia Vpol=Va-VbB Ib Vpol=Vc-VaC Ic Vpol=Va-Vb
AB Iab Vpol=-jVcBC
Ibc
Vpol=-jVa
CA Ica Vpol=-jVb
To illustrate this polarizing approach, consider the
lossless system for a configuration shown in Figure
4.17. Lossless systems contain only purely reactive
impedances and are also called 90 systems because the
phase current lags the phase voltage by 90. For a
single-line-to-ground fault on phase-C with zero fault
impedance, the phase-C current measured by relay Rs,
Isc, will lag the phase-C voltage of Vs by 90. The
resultant angle is 30. The phase of the polarizing
voltage is computed by subtracting the vectors Va-Vb
using rectangular coordinates as shown in (4.30) and
illustrated by Figure 4.24. Torque computations similarto (4.31) result in the largest positive torque value. Since
the fault is between relays Rs and Rr, the results are
identical except for the magnitude of the phase current.
If a single-line-to-ground fault occurs at F2, then the
current at relay Rs is 180 out of phase. This phase
reversal produces a negative result in the torque
computations. Using the corresponding Vpol listed in
Table 4.3 produces similar results for single-line-to-
ground faults for phases A and B.Vab V 0 V 240
V1 j 0 - - 0.5 - j 0.866V1.5 j 0.866 (4.30)V 30Tabc Iabc Vpol cos(VpolIabcMTA) (4.31)
where abc denotes phase A, B, or C and MTA is
the positive sequence line angleImaginary
=MTA IcVc
jVabVa
Real-120
o.732Va
Vab=130
oVb
Figure 4.24: Vector Diagram for Phase-C-to-GroundFault
4.2.7.2.6 Sequence polarizingOther choices for polarizing quantities include
symmetrical component voltages and currents as
described by (4.32 through (4.34. Symmetricalcomponent currents are popular for polarizing quantities
because they are relatively unaffected by load current.
Because of unbalanced lines and/or loads, only positive-
and negative-sequence currents are available during non-
faulted conditions. If a path exists to complete the circuit
for the ground current, the relay generates zero-sequence
voltages and currents for phase-to-ground faults.
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74Fault direction is computed using torque calculations
where the results are positive for forward faults and
negative for reverse faults. The magnitude can be
perceived as a confidence factor where inputs with
small magnitudes can produce unreliable results. Hence
low magnitude torque values should be ignored or used
only if no better information is available.For balanced systems at steady state, the relay generates
negative-sequence voltages and currents for all but
balanced three-phase faults. Negative-sequence voltages
can be weak to detect depending on the source
impedance behind the relay and on impedance between
the relay and the fault, as discussed in section and
illustrated in Figure 4.18 and Figure 4.19. A discussion
of each sequence polarizing quantity follows.I0 Ia Ib Ic and V0 Va Vb Vc Zero (4.32)I1 Ia a Ib a 2 Ic and Positive (4.33)V1 Va a Vb a Vc where a 1120
I2 Ia a2
Ib a Ic and Negativ (4.34)V1 Va a
2Vb a Vc e
Zero-sequence current polarizingReverse Forward
32TVIpol Ires cosIpolIreswhere (4.35)Ires Ia Ib Ic (4.36Table 4.4 and Table 4.5 show the phase angles for
forward and reverse phase-to-ground faults. The exact
angles computed are a function of the circuit and the
power system angle. Table 4.4 shows that the difference
between the polarizing and operating current results in
angles close to zero. The cosine of this angular
difference always produces a positive result with a
multiplier close to unity. Table 4.5 shows that the
difference is close to 180, which produces a negative
result with a multiplier that is also close to unity. Table 4.4: Polarizing and Operating Current Phase Angles for Forward
Ground and Two-Phase-to-Ground Faults UsingIresforIpolFault type Ipol Iop =Ires Ipol -IresAG -82.4 -81.2 -1.2BG 157.7 159.0 -1.2CG 37.5 38.7 -1.2ABG -143.6-143.2 -1.4CBG 97.6 98.7 -1.1
R R RIres #1
Ires #2A Phase
Fault #2 Bre
ake
rB Phase
To Source C Phase
Ipol
Fault #1To SourceCAG -23.0 -21.8 -1.2
Table 4.5: Polarizing and Operating Current Phase Angles for
Reverse Phase-to-Ground and Two-Phase-to-Ground FaultsFault Ipol Iop=Ires Ipol -IrestypeAG -73.9 115.5 -189.4
Figure 4.25: Polarizing Current Provided From a Delta-Grounded Wye Transformer
A polarizing current is available only if a zero-sequence
source is available, such as the neutral current in a
grounded wye transformer. The transformer need only
supply only a portion of the ground current. (4.35) and
(4.36) compute the direction as torque quantity with
both sign and magnitude. The phase of the polarizing
current does not change for faults at positions Fault #1
and Fault #2, illustrated in Figure 4.25, but the phase
angle of the residual current (3I0) reverses by 180.
BG 166.5 -4.7 171.2CG 46.2 124.6 170.8ABG -134.5 56.1 -190.6CBG 106.1 -66.8 172.9CAG -14.0 175.8 -189.8
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75Consider a fault at location F2 in the system shown in
Figure 4.26. Relay Rs may detect the fault forward or
reverse depending on the distance from Bus S to the
fault on line #2. More positive direction torque for relay
Rs results if the fault is on Line #2, closer to Bus R.
Faults at Bus R immediately behind relay R are
indistinguishable from faults at Bus R immediately infront of relay R. Depending on the fault impedance, line
unbalance, and load, faults at 50 percent of Line #2 may
produce positive torque. Relay systems using the
transformer neutral current for the polarizing quantity
may not perform satisfactorily for cases of multiple
parallel lines.Bus S Line #2 Bus R
ZL*m2 ZL*(1-m2)Is
REV sFORF2
Es SRC ZL*m3 Line #1 Zrr ErIs Ir
ZL*m1 ZL*(1-m1)Zt Rs Rr
ISpol Vs,Is Vr,IrRelay S Relay R
Figure 4.26: Single-Line Diagram of a System With TwoSources Connected by a Double-CircuitTransmission Line
4.1.5 Zero-sequence voltage polarizingEquation (4.37) provides the torque expression for zero-
sequence voltage polarizing using zero-sequence currentfor the operating quantity. AngleZL0 is the angle of the line
zero-sequence impedance. The residual current seen by the
relay is 3I0, which is equal to (Ia +Ib +Ic). Similarly, V0
equals (Va +Vb +Vc). If the source behind the relay is too
strong (low source impedance behind the relay), then a low
torque value results from small values of V0 because the
voltage divides, as discussed in section
direction. A major advantage of using (4.38) is that the
result is not sensitive to the magnitude of V0. This is
because the quantity V0/I0 is a constant since the current
is a linear function of the voltage. Another advantage of
this algorithm over(4.35) is that it doesnt require the
polarizing current generated by the transformer
grounded wye leg, which is not always available. ZL
0 Forward faultsRe3V0 3I0 results in
ZL0 (4.38) negative z0z0
3I02 values
4.1.6 Negative-sequence voltageand impedance polarizing
Use (4.40) for directional algorithms using negative-
sequence voltage for polarizing. Phase-to-phase-to-
ground and phase-to-ground faults generate negative-sequence quantities. This approach has the same
limitations as using zero-sequence voltage for
polarizing, except that it is not affected by zero-sequence
mutual coupling of parallel lines. Computing the
apparent negative sequence impedance between the relay
and the fault as shown in (4.43) overcomes the problem
of a weak polarizing quantity caused by low source
impedance behind the relay. xii xi xT32Q 3V2 3I2 cosV2I2ZL2, (4.39)-V2 is V2 shifted by 180When the negative-sequence source behind the relay
terminal is very strong, the negative-sequence voltage
(V2) at the relay can be very low, especially for remote
faults. To overcome low V2 magnitude, we can add a
compensating quantity that boosts V2 by (ZL2I2). The
constant, , controls the amount of compensation.Equation (4.40) shows the torque equation for a
4.3.2.4.T32V3V0 3I0 cosV0I0ZL0,-V0 is V0 shifted by 180 (4.37)
compensated negative-sequence directional element.
The term (ZL2I2) adds with V2 for forward faults and
subtracts for reverse faults. Setting too high can make
a reverse fault appear forward. This results when(ZL I ) is greater, but 180 out of phase with, theGuzman, Roberts, and Hou, using (4.38), present an
alternate directional algorithm based on zero-sequence
voltage current.xi The result calculated for Z0 is negative
for forward faults and positive for reverse faults. For an
explanation of this sign reversal from the torque
equations, see a discussion of similar expressions for
negative-sequence direction algorithms.x A threshold
impedance can limit the reach for faults in the forward
2 2measured V2 for reverse faults.T32Q ReV2ZL2 I2ZL2 I2 (4.40)Figure 4.27 shows the sequence network for a ground
fault at the relay bus. The relay measures IS2 for forward
faults and -IR2 for reverse faults. Use (4.41) to calculate
the negative sequence impedance, Z2, from V2 and I for
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76forward faults2 and (4.42) to calculate this impedance
for reverse SLG faults. Figure 4.27 shows this
relationship for a 90 (purely inductive) system.Z2 V2 ZS 2 (4.41)
IS2Z2 V2 ZL2 ZR2 (4.42)
IR2Bus S
Bus RS Z 1 Z
L REs 52 Es
Relay SFault
Positive Es ErSequenceBus S Bus RNetwork
Zs1 ZL1 1 ZR1Relay 1
NegativeIS2 V2Sequence Bus S IR2 Bus R
NetworkZs2 ZL2 1 ZR2
Relay 1Zero
Bus SSequence Bus RNetwork
Zs0 ZL0 ZR0Relay 1
RFFigure 4.27: Sequence Network for a Reverse Single-Line-
to-Ground (SLG) FaultDetermine the forward/reverse torque balance condition
by setting the left side of (4.40) equal to zero. Lettingz2
be equal to (ZL2I2) and solving for z2 at zero torque
results in (4.43). Recall that the (ZL2I2) term increases
the amount of V2 for directional calculations. This isequivalent to increasing the magnitude of the negative-
sequence source behind the relay location. The same
task is accomplished by increasing the forward z2
threshold.
ZL2 Forward faultsRe 3V2 3I2 ZL
2 result in negative (4.43) z 2 z2 values2
3I2The z2 directional element has all the benefits of both the
traditional and the compensated negative-sequence
directional element. It also provides better visualization
of how much compensation is secure and required. Set
the forward and reverse impedance thresholds based on
the strongest source conditions. Weak sources (high
source impedances) actually enhance negative-sequence
direction discrimination.As Figure 4.28 illustrates, the negative-sequence
directional element measures negative-sequence
impedance at the relay location. The relay then
compares this measurement to forward- and reverse-impedance thresholds, which are settings. The direction
is forward (in front of the relay) if the measured
negative-sequence impedance is less than the forward-
impedance threshold setting. The direction is reverse
(behind the relay) if the measured negative-sequence
impedance is greater than the reverse-impedance
threshold setting.R
SOURCE RSOURCE SZS ZL ZR
RF RF FORWARD FAULTREVERSE FAULTZ2MEASURED Z2 MEASURED
Z2 IMPEDANCE PLANE
+X2Z
R2+ Z
L2Z
2RZ
2F+R2
ZS2
Figure 4.28: Measured Negative-Sequence ImpedanceDetermines Direction
One advantage of the negative-sequence directional
element is the ability to operate correctly for both phase-
to-ground and phase-to-phase faults. However, like the
directional element using zero-sequence voltage or
current, it does not work well, if at all, with three-phase
faults. The impedance-based directional element is more
secure and reliable than a conventional negative-
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sequence directional element that calculates torque. The
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77impedance-based directional element is better for
faults at the end of long lines because they provide
minimal negative-sequence voltage for systems with
strong negative-sequence sources.4.1.7 Distance Relays (ANSI type 21)The example present in a previous section demonstrates
one case where the 52 relay tripped incorrectly because
of coordination problems under loaded conditions. The
same scenario can be made for the 50 and 67 relays as
well. Another problem with overcurrent relays is
providing backup protection under widely varying source
impedance conditions. Consider the system represented
by Figure 4.29 that has a maximum five-amp secondary
(from the CT) load current and a nominal 70 secondary
(from the PT) at the source Es1 or Es2. For this system,
assume that source impedance Zs1 is 1 and Zs2 is15
and either source must be capable of independentlycarrying the load. If the system has a three-phase fault
with1 line impedance from Bus S to the fault, the fault
current is equal to 70 V/1.9375 or 36 A. If the source,
Es1, is not connected, under the same faulted condition
the fault current is 70 V/15 or 4.67 A. Clearly the fault
current is less than the load current and the relay will not
trip. Distance relaying that measures the impedance to
the fault is less sensitive to load current, yet provides the
sensitivity needed for the problem cases just described.
fault. Distance relays offer the following advantages
over time-overcurrent relays: Greater instantaneous trip coverage
Lower sensitivity to source impedance changes
Better sensitivity to fault currents
Reduced sensitivity to load
Easier coordination with other distance relays
Electromechanical distance relays use torque-producing
coils to make trip contacts open or close.
Microprocessor-based relays calculate torque-like
quantities based on torque equations.4.3.2.6 Impedance Distance RelayingDistance relays use current to create operating torque and
voltage to generate restraining torque. When theoperating torque exceeds the restraining torque, the trip
contacts are closed. (4.44) shows the part of the basic
torque used for computing impedance for impedance-
type relays. As Figure 4.30 shows, this operation can be
perceived as a balanced beam system where voltage
produces the restraining torque and current the operating
torque. The balance point defines the fault/no fault
boundary of the relay where there is zero torque. (4.45)
defines the voltage and current for a fault on the
boundary.
Es1 Zs1Es2 Zs2
Bus S
RelayFault Load
T K1I K2 V (4.44)
K2 V
2 K1 I2 (4.45)
Balance BeamTrip Contacts
Figure 4.29: Fault Coverage Under Widely VaryingSource Impedance Conditions
All lines have impedance that is proportional to the length
of the line. The line angle is computed as the arctangent of
the ratio of reactive to resistive impedance at 60 Hz. For
overhead lines with 80 percent reactive and 20 percent
resistive series impedance, this angle is nominally 77
degrees. Although the magnitude of the impedance
increases with length, the line angle remains constant.
Distance relays are called such because they compute the
impedance to the fault, which is proportional to line length
between the relay and the
V IFigure 4.30: Balance Beam Torque ElementSince any positive nonzero torque produces a trip, equality
between the voltage and current terms in (4.45) determines
the sensitivity limit, resulting in zero torque. As (4.46)xiii
and (4.47) show, solving (4.45) for the zero torque case
provides the relationship for voltage and current as relates
to impedance. If the balance
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78impedance is a percentage of the line impedance,
then that percentage is called the reach of the relay.V
K1 Z (4.46)I K2T K2Z
2
I
2 V
2
(4.47)
Plotting of all possible values of voltage and current that
produce zero torque on an R-X (real-imaginary) diagram
forms a circle with the center at the origin and a radius
of Z, assuming that K2 is set to unity. The ratio of any
voltage and current combination that results in a point
inside the circle will produce torque, closing the trip
contact.Figure 4.31 illustrates the distance relay operation using
an R-X diagram. This figure shows the line impedance as
a line starting at the origin extending at the angle equal
to the line angle. The reach of the relay is a fraction ofthe total line impedance (labeled n in Figure 4.31). The
point where the circle-generated ratios of voltage to
current that produce zero torque and the line impedance
vector is called the reach of the relay. Reach is usually
denoted as a percent of the total line. Since the relay will
trip for any fault inside the circle, a directional-sensing
element must be added to restrict trips for faults in the
reverse direction.Impedance relays are inherently non-directional. One
means of making impedance relays directional is to
provide directional control with a type 32 relay as
discussed previously. (4.48) provides another method of
directional control where is the line angle and the
angle between the line impedance vector and the
difference between the voltage and current.. As long as
positive torque is produced, then the direction contacts
are closed, enabling the trip circuits. Assuming that K1,
the voltage, and the current are all nonzero, zero torque
is produced whenever (-) is 90. The directional
characteristic is shown in Figure 4.31 as the line
orthogonal to the line angle.T K1V I cos( ) (4.48)
jX Line lengthNo Trip Area = ZlRelay reach
Trip Area = nZlDirectional 90 o Trip Area
characteristic line
RForward
No Trip Area DirectionReverseDirection
Figure 4.31: RX Diagram for Impedance-Based DistanceRelay
Ohm distance relays are sensitive to fault resistance and
infeed from remote sources. As Figure 4.31 illustrates,
load into the source behind the relay makes relays under-
reach, while load current out of this source makes
impedance relays overreach. Techniques for overcomingthese sensitivities, where the relay operates on explicit
values of fault resistance and line reactance is discussed
in later sections.
Figure 4.32: Effects of Load Flow and Fault Resistance onApparent Impedance
MODIFIED IMPEDANCE RELAYSAs previously shown, impedance relay sensitivity is
uniform regardless of the direction of the derived
impedance. Shifting the center of the characteristiccircle along the line impedance vector reduces the
sensitivity to load currents as well as to faults in the
reverse direction. (4.49) describes the modified torque
equation. The constant C determines how far the center
of the circle shifts from the origin of the RX diagram as
shown in (4.50).
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79
T K1 I 2 K2(VCI) 2 (4.49)Z
V C K1 (4.50)I K2
CONCEPTS OF REACTANCE DISTANCE RELAYSFigure 4.33 shows a reactance distance relay that
combines an overcurrent element with a directional
element, as expressed in (4.51). K4 represents a
mechanical restraining spring and is the angle that the
current lags the voltage. By solving for zero torque, we
can rewrite (4.51) as (4.52). If we note that |Z| sin() is the
reactive component of Z and ignore the spring constant,
(4.53) relates the reactance to constants K1 and K3 for zero
torque. The relay uses only the reactive component of the
fault impedance to make the trip/no trip decision. Adding
the restraint from the mechanical spring moves the
characteristic line toward the real axis.T K1 I sin( ) K3 V I K4 (4.51)
K1 K4
sin ( ) Zsin ( ) (4.52)VI 3 K3 I
sin ( ) X K1 (4.53)Z K3
Line length = Zl = RljX + jXl
Relay Operating Relay reach =Characteristic nXl
No Trip Area No Trip AreaTrip Area Trip Area
Line angleR
Figure 4.33: Characteristics of a Reactance DistanceRelay
STARTING UNITSSince the impedance relay could operate for large
reactive loads, it requires a directional element that also
rejects such loads. This directional element is often a
voltage-restrained element. When used with a reactance
distance relay, the characteristic torque equation
becomes (4.54), where is positive for lagging current
and is the line impedance angle. Solving this equation
for the balance point, where the torque equals zero,
results in the expression shown in (4.54). Ignoring the
spring constant results in the expression for impedance
characteristic shown in (4.56).T K3 V Icos () K2 V K4 (4.54)V K3
cos ( ) K4 (4.55) ZK2 K2 V II
ZK 3cos () (4.56)K 2
Figure 4.34 shows the results of combining a starting
unit with a reactance relay. The trip area for this
characteristic is defined as the region inside the
starting characteristic circle, S, and below the
reactance line marked X1. The starting unit providesboth direction sensitivity and distance.
jX Line length= ZlNo Trip Area Relay reach
= nZlS
T2No Trip AreaX1
Trip Area T190
oLine angle
RNo Trip Area
Figure 4.34: Reactance Distance Relay CharacteristicsWith a Starting Unit
MHO DISTANCE RELAYThe characteristics of the mho distance relay are
identical to the starting unit described above. When the
mechanical spring constant are included, the diameter of
the circle, S, in Figure 4.34 as described by (4.56) is
independent of voltage and current magnitude except forlow levels of voltage or current. Low voltage levels are a
problem when the fault is very close to the relay origin,
causing the circle to collapse. In such cases, use a
memory voltage to conserve the prefault voltage
magnitude and phase.It is much easier to set mho ground distance elements
than quadrilateral ground distance elements. This is
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80because mho elements require fewer settings and are less
influenced by unequal source and line impedance angles.A mho element using positive-sequence memory-
polarization has a dynamic response that improves the
resistive fault coverage offered by the relay. Under weak
source conditions a mho element can offer betterresistive fault coverage for close-in faults than a
quadrilateral ground distance element.4.1.8 Advantages of using mho ground
distance elements over Quadralateral
Elements
The advantages are that they are easy to set, less
influenced by system nonhomogeneity than the
quadrilateral element and are capable of providing better
resistive fault coverage than the quadrilateral element
under certain system conditions.The disadvantages are that they provide limited resistive
fault coverage for faults at the end of the element reach
and limited resistive fault coverage for strong source
conditions hence are influenced by zero-sequence
mutual coupling.Typically, six distance elements detect six of the seven
possible types of faults as listed in Table 4.6.viii,xiv
The
three phase-to-phase fault elements also detect the
seventh fault type, three-phase-to-ground faults.Table 4.6: Voltages and Currents for Six Mho
Distance ElementsFault Voltage Current Polarization TorqueType V I Vpol T
A to Gnd Va Ia + k0 Ir Va1mem TagB to Gnd Vb Ib + k0 Ir Vb1mem TbgC to Gnd Vc Ic + k0 Ir Vc1mem TcgA to B VaVb IaIb -j Vc1mem TabB to C VbVc IbIc -j Va1mem TbcC to A VcVa IcIa -j Vb1mem TcaK0 = (Z0/Z11)/3 mem denotes memory voltage
Depending on the type of fault, use (4.1) or (4.24) to
compute the six torque values. The results are identical.ix
Both of these equations derive from (4.48). In (4.57) and
(4.59), m is the per-unit reach and ZL is the total line
impedance. Table 4.6 defines variables V, I, and Vpol.
As discussed in section 4.6.1.2, a voltage memory circuit
generates the polarizing voltages described by (4.60)
through (4.62). The unconventional shifting in these
three equations results in the conventional shifts required
for the positive-sequence component, but with better
transient response. viii Therefore, to shift by 240, shiftby 60 and negate the result (which is the same as adding
180 to the quantity already shifted by 60).TRem ZL I V whereVp (4.57)
Vpol complex conjugate (4.58)VpolTm ZL I V Vpol cosmZLIVVpol (4.59)Va1 Va a 1Vb a 2 1Vc (4.60)
3Vb1Vb a 1Vc a 21Va (4.61)
3Vc1Vc a 1Va a 21Vb (4.62)
3VOLTAGE PLANE REPRESENTATIONThe impedance plane with resistance and reactance as
coordinates is convenient for describing the operation of
impedance relays.Line length
= ZlImRelay reach M
90
oVI
)L
Z(m V
Line angleVpol Re
OS
Figure 4.35: Mho Relay Operations Described Using theVoltage Plane
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81Bus S
mZL1 Bus R ZR1ZS1 (1-m)ZL152 52
ES
Relay S Relay RE
RRF
Figure 4.36: Circuit Loops of a Faulted Power System NetworkQUADRILATERAL DISTANCE RELAY [6065]
XIVAlthough the distance relay is inherently directional
provided the reach is limited, it does have sensitivity
problems, particularly in the presence of fault
resistance. As Figure 4.37 shows, the quadrilateral relay
has characteristics that form a parallelogram, defined by
R1, R2, X, and 32Q. It is possible to work with zero-
and/or negative-sequence voltages and currents so that
the fault resistance results are less sensitive to positive-
sequence load.To provide greater fault resistance coverage for close-in
faults or systems with strong sources, set the resistive
reach to be far more sensitive than that of conventional
mho elements. It is also important to set the resistive
reach so that the negative-sequence voltages and
currents that result from normal operations or for out-of-
section faults will not trip the relay. There is no practical
reason for extending R2 to the left of the line defined by
the line angle, although R1 and R2 can be set to be
equal, for convenience. The resistance reach lines are
parallel to the line angle because, as we will show, the
fault resistance is computed independently of the line
resistance.If instrumentation errors are small, we can usually set
the upper reactance, X, to the same reactive reach as the
mho element. The directional element defines the bottom
of the parallelogram.Quadrilateral elements can detect both phase and ground
faults but require different algorithms. They can stretch
in all directions to provide the desired sensitivity and can
combine with conventional mho elements to generate the
tripping region shown in Figure 4.37. The characteristics
of this figure are reproducible where remote end infeed
is not significant, such as for radial lines.Small errors in voltage and current measurements can
cause errors in the reactance measurement with extended
resistive reach settings. Limiting the resistive reach with
respect to the reactance setting ensures that the relay is
measuring adequate signals for proper operation.
Differences in the source and line impedance angles can
cause the reactance element to overreach or under-reach.
It is common to reduce the reactive reach to obtain good
fault coverage for close-in faults with high fault
resistance and use a mho characteristic to get good line
reach coverage. Figure 4.38 shows this combination.
The following sections will discuss methods forproperly setting the quadrilateral for optimum restive
and reactive reach.jX
ZL1No Trip
AreaX
Relay reach= nZLl
R2Mho Circle
Trip areafor Trip area
mho forelement quadrilateral R1element
32Q Line angleR
Figure 4.37: Quadrilateral Relay Characteristics Laid Overthe Mho Relay Circle
jXZL1
No TripArea
XRelay reach= nZLl
Mho CircleTrip area
formho
element32Q Line angle Trip area
forquadrilateral
elementR
R2 R1Figure 4.38: Combined Mho and Quadrilateral
Characteristics4.1.9 Ground Fault Quadrilateral Fault
Detection
Ground fault protection using the quadrilateral element
requires computing both the reactance to the fault and
the fault resistance. For the sake of simplification at this
point, assume that the relay measures the total fault
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82current. We will relax this condition later in this section.
Figure 4.39 provides the basis for the set of loop
equations developed in (4.63) through (4.68). This
mathematics relates the phase voltage and current seen
by the relay to the positive-sequence line impedance that
is usually provided for setting relays.Va Ia mZs VMba VMca Ia RF, where (4.63)VMba m ZmIb, VMca m ZmIc (4.64)Va m Ia Zs ZmIa Ib IcZm Ia RF (4.65)ZL1Zs Zm , and Zm (ZL0 ZL1) / 3 (4.66)
ZL Ia Ia ZL0 ZL1 (4.67)Va m Ib Ic Ia R F1
3
Va m ZL1Ia k0Ir Ia R F, k0 ZL0 ZL13
ZL1
(4.68)
and Ir Ia Ib Ic
For quadrilateral elements, use two independent
equations to determine both the reactance to the fault
and the fault resistance. Derive both equations from the
loop diagram shown in Figure 4.40. If either the switch
at Bus R is open or the fault resistance is zero, the
impedance is simply the voltage divided by the current.
In this case neither the source impedance nor the
impedance beyond the fault are of any consequence.
Beginning with the result of (4.68) we can use (4.69) to
solve for the fault resistance and (4.70) for the reactance
to the fault. Note that in both equationsIa is identical tothe total fault current in both magnitude and angle, with
angle being the critical factor to make (4.77) true. For
this case alone,Zdoes equal V/I. xiii
Za VA IA VMBA VMCA VS + -+ - F}
EA R IFF
mZasZb VB IB L VMAB VMCB
S+ - + -
}EB
mZbsLZc V IC V MAC V MBC
CS + - + -}
EC
mZcsLFigure 4.39: Single-Line-to-Ground Fault on a Three-
Phase System
ImVaZL1 Ia k0 Ir, where k0 ZL0 ZL1 (4.6RF
3ZL1ImIaZL1Iak0Ir 9)and Ir Ia Ib Ic
X1 ImVa I a , whereZL1 ZL1 (4.7 ImZL1Iak0Ia0Ia ZL1 0)
VSA ISA+k0Iress VL IRA+k0Iresr VRA
ZS } } ZRESA
~
I RFVF ~ ERABUS S mZ1L F (1-m)Z1L BUS RFigure 4.40: Loop Diagram for a Phase-to-Ground FaultIf the switch at VRA is closed and RF is not zero, then the
relay at Bus S can no longer measure the total fault
current and the phase angle ofIa is no longer co-linear
with the phase angle ofIf. Without knowing the faultcurrent from the remote end, we must approximate the
fault current. A current distribution factor (CDF) relates
the total fault current to the measured current, ISA. The
sequence component diagram in Figure 4.41 shows that
the total fault current divides according to the zero-
sequence impedance between the fault and the SandR
ends of the line. For the zero-sequence CDF expressed in
(4.71) to be accurate, we must know the distance to the
fault as well as the source impedances at both ends of
the lines. If the system is co-linear (i.e. the phase angle
of the source and line impedances are all equal) the CDF
is a scalar quantity. This fault distance data is provided
by (4.88).
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83
Es ErZs1 m*ZL1 (1-m)*ZL1 Zr1
Vs Is2 Vf2 Ir2 2
Zs2 m*ZL1 (1-m)*ZL1 Zr2Rs Ia = I1=I2=I0
Is0 Vf0 Ir0Zs0 m*ZL0 (1-m)*ZL0 Zr0
Rs 3RF
Figure 4.41: Symmetrical Component Diagram for a
Single-Line-to-Ground Fault
1 mZL0Zr0 (4.71)CDFZs ZL Zr
0 0 0 Load current also affects the accuracy of the results of
(4.69) and (4.70). Reduce this problem by making the
approximation that the faulted phase current, Ia, used to
compute the fault current, is equal to two-thirds the sum
of the faulted phase zero- and negative-sequence
current as shown in (4.72). Equation (4.73) shows the
final result for calculating the fault resistance.Ia 3 Ia0 Ia2 (4.72)
RF ImVaZL1Ia k0 Ir (4.73)3
Im Ia Ia CDFZL1Ia k0 Ir2 0 2 0
Figure 4.41 shows that the negative-sequence fault current
is equal to the zero-sequence current at the fault for single-
line-to-ground faults. (4.73) also shows that the CDF has a
magnifying effect on the computed fault resistance. As the
fault moves toward the remote end, the CDF becomes
smaller. A decreasing CDF results in a largerRFas
computed by (4.73). The net effect is that covering the
same fault resistance for the entire length of the line
requires increased resistive fault coverage. It is
easier to detect a one-ohm fault immediately in front of the
relay than the same fault at the remote end of the line.Only the phase of the polarizing quantity allows us to
extract the variable we wish to solve for in (4.68). This
is done by making the coefficient of the variable that is
to be isolated and removed real in the loop equation andtaking only the imaginary part of the equation. Since the
current is common for faults on radial lines, (4.79) and
(4.80).A system is completely homogeneous when the line and
source angles are equal in all three sequence networks. The
system is also considered homogeneous if the source and
line impedances associated with the sequence current used
by the reactance element for polarizing references have the
same angle. For example, in a reactance element that uses
zero-sequence current as a polarizing reference, consider
only the zero-sequence network. In a reactance element that
uses negative-sequence current as a polarizing reference,
consider only the negative-sequence network. Here, we
restrict the discussion to reactance elements that use zero-
sequence polarization.A system is nonhomogeneous when the source and line
impedance angles are not the same. In a nonhomogeneous
system, the angle of the total current in the fault is different
from the angle of current measured at the relay. For this
case, the CDF is no longer a scalar quantity but has a phase
angle as well. For a bolted fault (a condition that assumes
no resistance in the fault), a difference between the fault
current angle and the current angle measured at the relay isnot a problem. However, if there is fault resistance, the
difference between the fault and relay current angles can
cause a ground distance relay to severely underreach or
overreach.Figure 4.40 shows that we can represent the phase
voltage measured by a relay at Bus S as the sum of two
voltage drops: the voltage drop across the transmission
line ground loop impedance and the voltage drop across
the fault resistance. (4.74) gives